Stability and periodicity in coupled Pinney equations
The author studies the correspondence (established in an earlier paper) between solutions of the coupled Pinney equations \(d^ 2x/dt^ 2+\omega^ 2(t)x=-\alpha xy^{-4}+\beta x^{-3}\), \(d^ 2y/dt^ 2+\omega^ 2(t)y=-\gamma yx^{-4}+\delta y^{-3}\) and the associated Hill's equations. It is shown that stability (periodicity) of the general solution of the linearized system (Hill's equations) is sufficient for stability (periodicity) of solutions to the original nonlinear system.
scientific article; zbMATH DE number 97340
scientific article